Distributionally robust optimization via regularized robust optimization

doi:10.1080/02331934.2026.2614724

Distributionally robust optimization via regularized robust optimization

2026-01-01

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DOI：10.1080/02331934.2026.2614724

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In this paper, we aim at solving distributionally robust optimization problems motivated by application in robust machine learning. For this, we propose a novel SGD-type computationally tractable and provably convergent algorithm without any need of convexity/concavity assumptions unlike most works in the literature. To achieve this, the distributionally robust optimization is first approached with a point-wise counterpart at controlled accuracy. Second, to avoid solving the generally intractable inner maximization problem, we use entropic regularization and Monte Carlo integration. The approximation errors induced by these steps are quantified and thus can be controlled by making the regularization parameter decay and the number of integration samples increase at an appropriate rate. This paves the way to minimizing our objective with stochastic (sub)gradient descent whose convergence guarantees to critical points are established. To support these theoretical findings, compelling numerical experiments on simulated and benchmark datasets are carried out and confirm the practical benefits of our approach.

Keywords:

Robust optimization

DRO

smoothing

regularization

robust learning

neural networks

SGD

Distributionally robust optimization via regularized robust optimization

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